GEOMETRY & GEOMETRIC SHAPES

OCTAGON

OCTAGON PROBLEM:   A landscaper wants to built octagon shaped planters that have a 24 inches(61cm) inside dimension.

STEP 1: The planter's ~perimeter is the inside dimension multiplied by PI (π).

NEXT:  We multiply 24 times PI (24 * 3.14159) = 75.398

STEP 2:  Because there are 8 sides to an octagon we divide 75.388 by 8. (75.388 ÷ 8 = 9.424) or (~9 7/16 inches).

STEP 3:   We need to know what angle the side segments need to be cut at.
There are 360 "Exterior" degrees in an octagon ~perimeter.

Next:  we divide 360 by 16 (because there are two 22.5° angles in each segment.)

(360 ÷ 16 = 22.5) Degrees

See the Illustration below:

NOTE: I know the formula for an octagon perimeter is P = 8a (where the segments is labeled a. However, if the segment length is unknown or difficult to find. Using a circle perimeter formula ( π D) or 2πr will give a surprisingly close answer to segment length.

This is not an idle calculation. The image above is an actual octagon I built and used as a concrete form to make pads to put my trash cans on. As one can see the joints are very accurate. only the tie down ratchet holds the boards together.

There are (45 * 8) = 360 exterior degrees and (135 * 8) = 1080 interior degrees in an octagon.